Non-steady peristaltic propulsion with exponential variable viscosity: a study of transport through the digestive system

A theoretical study is presented for transient peristaltic flow of an incompressible fluid with variable viscosity in a finite length cylindrical tube as a simulation of transport in physiological vessels and biomimetic peristaltic pumps. The current axisymmetric analysis is qualitatively similar to two-dimensional analysis but exhibits quantitative variations. The current analysis is motivated towards further elucidating the physiological migration of gastric suspensions (food bolus) in the human digestive system. It also applies to variable viscosity industrial fluid (waste) peristaltic pumping systems. First, an axisymmetric model is analysed in the limit of large wavelength (\[a < < \lambda \rightarrow \infty \] a<<λ→∞) and low Reynolds number (\[Re\rightarrow 0\] Re→0) for axial velocity, radial velocity, pressure, hydromechanical efficiency and stream function in terms of radial vibration of the wall (\[h \] h), amplitude of the wave (\[\phi \] φ), averaged flow rate (\[\bar {>Q} \] Q¯) and variable viscosity (\[\mu ( r )\] μr). Subsequently, the peristaltic flow of a fluid with an exponential viscosity model is examined, which is based on the analytical solutions for pressure, wall shear stress, hydromechanical efficiency and streamline patterns in the finite length tube. The results are found to correlate well with earlier studies using a constant viscosity formulation. This study reveals some important features in the flow characteristics including the observation that pressure as well as both number and size of lower trapped bolus increases. Furthermore, the study indicates that hydromechanical efficiency reduces with increasing magnitude of viscosity parameter.